Ji Young Choi

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 2, Pages 40-48

DOI: 10.7546/nntdm.2019.25.2.40-48

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## Details

### Authors and affiliations

*Department of Mathematics, Shippensburg University of PA
1871 Old Main Dr., Shippensburg PA 17257, United States
*

### Abstract

Let *b* be an integer greater than 1 and *g* = *b* − 1. For any nonnegative integer *n*, we define *indispensable digits *in the base-*b* representation of *n* so that we can calculate the digit sum of the base-*b* representation of *g* · *n*: Instead of adding every digit in it, we multiply *g* by the number of the indispensable digits in the base-*b* representation of *n*. Then, we find the formula to calculate the digit sum of *g* · *n* + *r* using the number of indispensable digits in *n*, for any nonnegative integers *n* and *r* with 0 < *r* < *g*.

### Keywords

- Digit sum
- Indispensable digits
- Digit sum congruence
- Casting out nines
- Divisibility test

### 2010 Mathematics Subject Classification

- 11A63
- 11A07

### References

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- Atanassov, K. (2015). A digital arithmetical function and some of its applications, Proceedings of the Jangjeon Mathematical Society, 18 (4), 511–528.
- Datta, D. & Singh, A. N. (1962). History of Hindu Mathematics: A Source Book, Asia Publishing House, Bombay, Available online at: https://ia801600.us.archive.org/20/items/HinduMathematics/HinduMathematics.pdf.
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## Cite this paper

APAChoi, J. Y. (2019). Indispensable digits for digit sums. Notes on Number Theory and Discrete Mathematics, 25(2), 40-48, doi: 10.7546/nntdm.2019.25.2.40-48.

ChicagoChoi, Ji Young “Indispensable digits for digit sums.” Notes on Number Theory and Discrete Mathematics 25, no. 2 (2019): 40-48, doi: 10.7546/nntdm.2019.25.2.40-48.

MLAChoi, Ji Young “Indispensable digits for digit sums.” Notes on Number Theory and Discrete Mathematics 25.2 (2019): 40-48. Print, doi: 10.7546/nntdm.2019.25.2.40-48.